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The lengths of the diagonals of a rhombus are 24 cm and 32 cm. Calculate the length of the altitude of the rhombus. Question 9. Question Are the two triangles similar? Find whether XY BC or not. Find the height of the wall where the top of the ladder touches it. DF OC Proof. A vertical pole of length 8 m casts a shadow 6 cm long on the ground and at the same time a tower casts a shadow 30 m long. Find the height of tower.
State whether the given pairs of triangles are similar or not. In case of similarity mention the criterion. CP Hence Proved.
ABCD is a rhombus. The diagonals of trapezium ABCD intersect each other at point o. Show that ABCD is a trapezium. ABCD is a trapezium. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
State and prove converse of Pythagoras theorem. Give two different examples of pairs of i similar figures. State whether the following quadrilaterals are similar or not. In the given figure i and ii , DE BC. Find EC in i and AD in ii. Show that EF QR. Show that BC QR. Using B. Recall that your have proved it in class IX Solution:. Using converse of B. Recall that your have done it in class IX Solution:.
State which pairs of triangles in the given figures are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form :.
Prove that: Solution:. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower. If the areas of two similar triangles are equal, prove that they are congruent.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians. Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals. Areas of these triangles are in the ratio a 2 : 3 b 4 : 9 c 81 : 16 d 16 : Sides of triangles are given below.
Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse. CD Solution:. ABC is an isosceles triangle right angled at C. ABC is an equilateral triangle of side la. Find each of its altitudes. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. A ladder 10 m long reaches a window 8 m above the ground. A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end.
How far from the base of the pole should the stake be driven so that the wire will be taut? An aeroplane leaves an airport and flies due north at a speed of km per hour.
At the same time, another aeroplane leaves the same airport and flies due west at a speed of km per hour.
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